Standards Map

Mathematics | Course : Model Algebra I (Traditional Pathway)

Domain - The Real Number System

Cluster - Use properties of rational and irrational numbers.

[AI.N-RN.B.3] - Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.

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Resources:

• Irrational number
  A number that cannot be expressed as a quotient of two integers, e.g.,√2 . It can be shown that a number is irrational if and only if it cannot be written as a repeating or terminating decimal.
• Rational number
  A number expressible in the form ^a∕_b or – ^a∕_b for some fraction ^a∕_b. The rational numbers include the integers.

MCAS Items:
• 2024 Spring Release - Mathematics - Grade 10 - Item 2
• 2023 Spring Release - Mathematics - Grade 10 - Item 11
• 2021 Spring Release - Mathematics - Grade 10 - Item 11
• 2019 Spring Release - Mathematics - Grade 10 - Item 19

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Predecessor Standards:

• 8.NS.A.1
  Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.
• 8.EE.A.2
  Use square root and cube root symbols to represent solutions to equations of the form x² = p and x³ = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.

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Successor Standards:

No Successor Standards found.

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Same Level Standards:

• AII.N-CN.A.1
  Know there is a complex number i such that i² = −1, and every complex number has the form a + bi with x-a and b real.
• AII.A-APR.D.6
  Rewrite simple rational expressions in different forms; write ^a(x)/_b(x) in the form q(x) + ^r(x)/_b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system.